# N-body study of 55 Cancri

## N-body study of 55 Cancri

Another study of 55 Cancri...

Nelson et al. "The 55 Cancri Planetary System: Fully Self-Consistent N-body Constraints and a Dynamical Analysis"

http://arxiv.org/abs/1402.6343

New estimates for the density of 55 Cnc e, and the period/eccentricity of the outermost planet are now closer to those of Jupiter.

55 Cnc f orbital eccentricity is still somewhat uncertain but seems to be coming out quite a lot lower than previous estimates.

Nelson et al. "The 55 Cancri Planetary System: Fully Self-Consistent N-body Constraints and a Dynamical Analysis"

http://arxiv.org/abs/1402.6343

New estimates for the density of 55 Cnc e, and the period/eccentricity of the outermost planet are now closer to those of Jupiter.

55 Cnc f orbital eccentricity is still somewhat uncertain but seems to be coming out quite a lot lower than previous estimates.

**Lazarus**- dG star
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## Re: N-body study of 55 Cancri

Penn State University news release

http://science.psu.edu/news-and-events/2014-news/Ford4-2014

http://science.psu.edu/news-and-events/2014-news/Ford4-2014

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## Re: N-body study of 55 Cancri

Red noise in the data appear to drown out signals from n-body perturbations.

Improving robustness of exoplanetary orbital fits through a regularization of the white and red Doppler noise models. Hints of a 13-year star-spot activity cycle of 55 Cancri

http://arxiv.org/abs/1407.8482

Improving robustness of exoplanetary orbital fits through a regularization of the white and red Doppler noise models. Hints of a 13-year star-spot activity cycle of 55 Cancri

http://arxiv.org/abs/1407.8482

We consider the impact of the Doppler noise model on the statistical robustness of the exoplanetary radial-velocity fits. We show that the traditional model of the Doppler noise with an additive jitter can generate large non-linearity effects, decreasing the reliability of the fit, especially in the cases when a correleated Doppler noise is involved. We introduce a regularization of the additive noise model that can gracefully eliminate its singularities together with the associated non-linearity effects.

We apply this approach to Doppler time-series data of several exoplanetary systems. It demonstrates that our new regularized noise model yields orbital fits that have either increased or at least the same statistical robustness, in comparison with the simple additive jitter. Various statistical uncertainties in the parametric estimations are often reduced, while planet detection significance is often increased.

Concerning the 55 Cnc five-planet system, we show that its Doppler data contain significant correlated ("red") noise. Its correlation timescale is in the range from days to months, and its magnitude is much larger than the effect of the planetary N-body perturbations in the radial velocity (these perturbations thus appear undetectable). Characteristics of the red noise depend on the spectrograph/observatory, and also show a cyclic time variation in phase with the public Ca II H&K and photometry measurements. We interpret this modulation as a hint of the long-term activity cycle of 55 Cnc, similar to the Solar 11-year cycle. We estimate the 55 Cnc activity period by 12.6 (+2.5,-1.0) yrs, with the nearest minimum presumably expected in 2014 or 2015.

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## Re: N-body study of 55 Cancri

Also does not confirm the 9.8-day signal from Baluev (2013).

Eccentricity of f is found to be higher than the previous analysis of Nelson et al. (2014), but still consistent with zero.

Finally, we note that in (Baluev 2013b) we have done a brief period analysis on the 55 Cnc Lick RV data from (Fischer et al. 2008), claiming an uncertain detection of an additional 9.8 d signal. The period of 9.8 d was not confirmed by Nelson et al. (2014) with updated data, and now we do not confirm it too. This 9.8 d signal now looks like an artifact of the red noise that was ignored in (Baluev 2013b).

Eccentricity of f is found to be higher than the previous analysis of Nelson et al. (2014), but still consistent with zero.

Comparing this fit with the fit by Nelson et al. (2014), we do not spot any significant difference, except for the planetfeccentricity,e_{f}. We obtaine_{f}≈ 0.3, while Nelson et al. (2014) give an almost zero value. This change appears due to the red-noise model. More detailed investigation shows that thise_{f}is still consistent with zero: we obtain only ~ 0.5-sigma deviation according to the relevant likelihood-ratio statistic. In fact, this eccentricity appears very poorly determined, offering only an upper limit ofe_{f}≲ 0.5.

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